Both informed and uninformed search strategies are commonly used in problemsolving applications. However, they have distinct properties that determine when it may be advisable to prefer one over the other. Consider the search problem below, where A is the initial state, and D is the goal state. The optimal path is that with the lowest accumulated path cost. a) Uniform-Cost-Search (UCS) is an algorithm that uses the path cost to determine which nodes to explore in sequence. i) Assuming a tree-search implementation, give the sequence of nodes in which UCS is going to explore the tree. ii) Did UCS find the optimal solution for this problem? iii) Given positive path cost for any given search problem, is UCS guaranteed to always find an optimal solution? Explain